We review recent evidence indicating that researchers in experimental psychology may have used suboptimal estimates of word frequency. Word frequency measures should be based on a corpus of at least 20 million words that contains language participants in psychology experiments are likely to have been exposed to. In addition, the quality of word frequency measures should be ascertained by correlating them with behavioral word processing data. When we apply these criteria to the word frequency measures available for the German language, we find that the commonly used Celex frequencies are the least powerful to predict lexical decision times. Better results are obtained with the Leipzig frequencies, the dlexDB frequencies, and the Google Books 2000-2009 frequencies. However, as in other languages the best performance is observed with subtitle-based word frequencies. The SUBTLEX-DE word frequencies collected for the present ms are made available in easy-to-use files and are free for educational purposes.

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise to dynamical and geometric phases every orbit is weighted by. We also present an analogous approach to the Pauli equation which we analyse in two different limits.

Recently, researchers reported a bias for placing agents predominantly on the left side of pictures. Both hemispheric specialization and cultural preferences have been hypothesized to be the origin of this bias. To evaluate these hypotheses, we conducted a study with participants exposed to different reading and writing systems: Germans, who use a left-to-right system, and Israelis, who use a right-to-left system. In addition, we manipulated the degree of exposure to the writing systems by testing preschoolers and adults. Participants heard agent-first or recipient-first sentences and were asked to draw the content of the sentences or to arrange transparencies of protagonists and objects such that their arrangement depicted the sentences. Although preschool-age children in both countries showed no directional bias, adults manifested a bias that was consistent with the writing system of their language. These results support the cultural hypothesis regarding the origin of spatial-representational biases.

We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums over periodic orbits on the graph. This includes trace formulae with, respectively, absolutely and conditionally convergent periodic orbit sums; the convergence depending on properties of the test functions used. We also prove a trace formula for the heat kernel and provide small-t asymptotics for the trace of the heat kernel.

We investigate the Dirac equation in the semiclassical limit → 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.